Categorical language and geometrical methods in Machine Learning

In Machine Learning we develop mathematical methods for modeling data structures, which express the dependency between observables, and design efficient algorithms for estimation of such dependency. The most advanced part of Machine Learning is statistical learning theory that takes into account our incomplete information of observables, using measure theory and functional analysis. In this way we not only unveil hidden structure of data but also make a prediction for the future. In my lecture I shall consider basic problems in statistical learning theory and demonstrate the efficiency of categorical language, manifested, in particular, in terms of probabilistic morphisms, and the use of geometric constructions, e.g. diffeological Fisher metric, in solving these problems.